A pharmacist must calculate the shelf life for an antibiotic. The antibiotic is

Question

A pharmacist must calculate the shelf life for an antibiotic. The antibiotic is stored as a solid and a fresh solution must be prepared for the patient. The antibiotic is unstable in solution and decomposes according to the following data Time (days) [Antibiotic] (mol/L) 0 10 20 30 40 1.24 x 102 92 x 10-2 68 x 102 50 x 102 37 x 10-2 This is a first order process Question 1 Calculate the half-life for the antibiotic. The units should be in days and should be calculated to three significant figures. Submit AnswerTries 0/45 Question 2 If you start with a 1.0 M solution, how long would it take for 67 % of the antibiotic to decompose? The answer should be in days and should be calculated to three significant figures Submit Answer Tries 0/45

Explanation / Answer

1)

for first - order process :

rate constant k = 1/t ln (Ao / At)

   k = 1/ 10 ln (1.24 / 0.92)

k = 0.0298 day-1

half - life = 0.693 / k

half - life = 0.693 / 0.0298

half - life = 23.2 days

2)

k = 1/t ln (Ao / At)

0.0298 = 1/ t ln (100 / 33)

t = 37.2

time taken = 37.2 days

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